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R. Lednicky: Joint Institute for Nuclear Research, Dubna, Russia

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Correlation radiifromA FAST HADRON FREEZE-OUT GENERATOR

( FASTMC )

R. Lednicky: Joint Institute for Nuclear Research, Dubna, Russia

I.P. Lokhtin, A.M. Snigirev , L.V. Malinina: Moscow State University, Institute of Nuclear Physics, Russia

Iu.A. Karpenko,Yu.M. Sinyukov: Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

The predictions for correlation radii in the central Pb+Pb collisions for LHC GeV

(PRC 74 064901(2006))

http://uhkm.jinr.ru

Outline

1. Introduction- motivation.

2. Model parameters.

3. Physical framework of the model .

4. Predictions for LHC

Introduction-Motivation

- LHC very high hadron multiplicities
- fairly fast MC- generators for event simulation required
- FASTMC- fast Monte Carlo procedure of hadron generation:
- We avoid straightforward 6-dimentional integration
- ~100% efficiency of generation procedure
- Matter is thermally equilibrated. Particle multiplicities are determined by the
- temperature and chemical potentials. Statistical model. Chemical freeze-out.
- Particles can be generated on the chemical (Tth=Tch) or thermal freeze-out
- hypersurface is represented by a parameterization (or a numerical solution of
- the relativistic hydrodynamics).

- Various parameterizations of the hadron freeze-out hypersurface and flow velocity

- Decays of hadronic resonances (from u,d and s quarks) are included

- The C++ generator code is written under the ROOT framework.

Model parameters for central collisions:

- 1.Thermodynamic parameters at chemical freeze-out: Tch, {µB, µS, µQ}
- 2. If thermal freeze-out is considered: Tth , µπ-normalisation constant
- 3.As an option, strangeness suppressionγS < 1
- 4. Volume parameters:
- τ-the freeze-out proper time and its standard deviation Δτ (emission duration)
- R- firebal transverse radius
- 5. -maximal transverse flow rapidity for Bjorken-like parametrization
- ηmax -maximal space-time longitudinal rapidity whichdetermines the rapidity interval [- ηmax, ηmax] in the collision center-of-mass system.
- To account for the violation of the boost invariance, an option corresponding to the substitutionof the uniform distribution of the space-time longitudinalrapidity by a Gaussian distribution in η.
- 8. Option to calculate T, µBusing phenomenological parametrizations

Physical framework of the model: Hadron multiplicities

1.We consider the hadronic matter created in heavy-ion collisions as a hydrodynamically expanding fireball with the EOS of an ideal hadron gas.

2. “concept of effective volume” T=const and µ=const the total yield of particle species is: , total co-moving volume, ρ-particle number density

3.Chemical freeze-out : T, µi = µB Bi + µS Si + µQ Qi ; T, µB –can be fixed by particle ratios, or by phenomenological formulas

4. Chemical freeze-out: all macroscopic characteristics of particle system are determined via a set of equilibrium distribution functions in the fluid element rest frame:

Physical framework of the model: Thermal freeze-out

- The particle densities at the chemical freeze-out stage are too high to consider
- particles as free streaming and to associate this stage with the thermal freeze-out

2. Assumption of the conservation of the particle number ratios in between the chemical and thermal freeze-out :

3. In the Boltzmann approximation:

Particles (stable, resonances) are generated on the thermal freeze-out hypersurface, the hadronic composition at this stage is defined by the parameters of the system at chemical freeze-out

Physical framework of the model: Hadron momentum distribution

We suppose that a hydrodynamic expansion of the fireball ends by a sudden system breakup

at given T and chemical potentials. Momentum distribution of produced hadrons keeps

the thermal character of the equilibrium distribution.

Cooper-Frye formula:

Freeze-out surfaceparameterizations

1. The Bjorken model with hypersurface

2. Linear transverse flow rapidity profile:

3. The total effective volume for particle production at

Predictions for LHC

We considered the naive ``scaling'' of the existingphysical picture of heavy ion interactions over two order ofmagnitude in to the maximal LHC energy

GeV

We performed:

- FASTMCfitting of theexisting experimental data onmt-spectra, particle ratios, rapidity densitydN/dy, kt-dependence of the correlation radiifrom

SPS (= 8.7 - 17.3GeV)to RHIC (= 200GeV)

-The linear extrapolation of the model parametersin to LHC

GeV

For LHC energies we have fixed the thermodynamic parameters at chemical freeze-outas the asymptotic ones:Tch=170MeV,µB=0, µS=0, µQ=0 MeV.

Predictions for LHC

SPS (= 8.7 - 17.3GeV)

▲RHIC (= 200GeV)

LHC ( = 5500 GeV)

■

○

Predictions for LHC: Conclusions

The extrapolated values :

R ~ 11fm, τ ~ 10fm/c, Δτ~ 3.0fm/c,

~ 1.0, Tth ~ 130MeV.

Tch=170MeV,µB=0, µS=0, µQ=0 MeV

dN/dy ~ 1400 twice larger than at RHIC

= 200GeV

in coincidence with the naive

extrapolation of dN/dy.

These parameters yield only a small

increase of thecorrelation radii

Rout, Rside, Rlong